HOW DEMOCRACY WORKS (OR WHY PERFECT ELECTIONS SHOULD ALL END IN TIES)

Danny Hillis, physicist and computer scientist, brings together, in full circle, many of the ideas circulating among third culture thinkers: Marvin Minsky's society of mind; Christopher G. Langton's artificial life; Richard Dawkins' gene's-eye view; the plectics practiced at Santa Fe. Hillis developed the algorithms that made possible the massively parallel computer. He began in physics and then went into computer science — where he revolutionized the field — and he brought his algorithms to bear on the study of evolution. He sees the autocatalytic effect of fast computers, which lets us design better and faster computers faster, as analogous to the evolution of intelligence. At MIT in the late seventies, Hillis built his "connection machine," a computer that makes use of integrated circuits and, in its parallel operations, closely reflects the workings of the human mind. In 1983, he spun off a computer company called Thinking Machines, which set out to build the world's fastest supercomputer by utilizing parallel architecture.

The massively parallel computational model is critical to an understanding of today's revolution in human communication. Hillis's computers, which are fast enough to simulate the process of evolution itself, have shown that programs of random instructions can, by competing, produce new generations of programs — an approach that may well lead to the first machine that truly "thinks." Hillis's work demonstrates that when systems are not engineered but instead allowed to evolve — to build themselves — then the resultant whole is greater than the sum of its parts. Simple entities working together produce some complex thing that transcends them; the implications for biology, engineering, and physics are enormous.

Here is a simple, successful election. The graph shows how many voters are at each point on the political spectrum. It also shows the positions of the candidates. The Good candidate is the one whose opinions are closest to the will of the voters. Voters choose the candidate that is closest to their own position, so the Good candidate wins.

The dividing line shows where the vote splits. Voters to the left of the line will vote for the Good candidate, voters to the right of the line will vote for the Bad candidate.

Of course I don't mean that Left is Good and Right is Bad. The picture works the same way if we flip it around.

Either way, the Good candidate wins, and the election is successful. Some voters are unhappy, but even more voters would have been unhappy if the Bad candidate had won.

In some cases most of the voters may be unhappy with the results. This depends on the shape of the opinion curve. Here is one type of unpleasant outcomes:

In this case the voters' opinions are highly polarized, and the candidates are uncompromising. Almost half the population will be extremely unhappy with the result.

Here is a less unhappy variation:

In this case voters' opinions are highly polarized, but the candidates' positions represent a compromise. Almost all of the voters are relatively unhappy. As unpleasant as these outcomes may seem, they still represent successes of the democratic process. No other choice of leader would have led to a better result.

If we add a third candidate, the democratic process does not even necessarily produce the best result.

In this case the Spoiler candidate takes away enough votes from the Good candidate to allow the Bad candidate to win. This is very likely to happen if there are three parties.

In a many-party system, the voters are more likely to be happy with the choice of candidates, because they can find a candidate that is close to their own position. Unfortunately, the voters are less likely to be happy with the result of the election, because it will not necessarily choose the Best candidate. This situation is even worse when there are many viable candidates.

In a multiple party vote, each voter will be able to choose a candidate with opinions close to his or her own, but the candidate who gets elected will be the one that has the broadest constituency, not the one who best represents the will of the all the voters. Because the worst candidates pick up the outliers, it is relatively easy for a very bad candidate to win.

Let's go back to the case of only two parties.

If the candidates are willing to be flexible, then either candidate can gain votes by moving toward the Best Position. The Best Position is where an equal number of voters are to the left and to the right. A candidate in the Best Position is unbeatable. A candidate in the Best Position also does the best job of making the voters happy, or at least making them less unhappy than they would be otherwise.

If the candidates have some flexibility in their opinions and good information about what the voters want, they will move their own positions towards the Best Position, because it increases their chances of being elected. The closer one candidate moves towards the Best Position, the closer the other candidate will have to move to remain electable. With good pre-election polling, both candidates will be able to determine very accurately how much they need to move. If they are both willing to adjust their positions near the Best Position the outcome of the race will depend on the accuracy of the polling. If the polling is perfect, all elections will end in near ties.

This process of adjusting position in response to polling may seem to compromise the integrity of the candidate, but it does produce candidates whose opinion is very close to the Best Position. This may be regarded as a successful outcome, because a candidate in the Best Position also does the best job of making the voters happy.

Actually, a winner in the Best Position doesn't necessarily make many voters happy; it just makes them less unhappy than they would be with a different winner. In the previous illustrations, the best position was also the most popular position. This is not always the case.

In this final example, the voters are polarized and the Best Position is highly unpopular. Still, it represents the most electable position, and also the position that makes the fewest people very unhappy. This is the best result that any system can produce.

So in the end, two-party democracy is not necessarily good at giving voters a chance to elect a candidate that they like. If the polls are very accurate and the candidates are flexible, a successful election is likely to produce two candidates whom the voter will regard as equally imperfect. The election results will be very close.

For all its problems, the two-party democracy does a good job of producing and selecting candidates that represent an acceptable compromise between a wide spectrum of opinions. If the process is working well, then by the time of the election many voters may feel that they have very little real choice. This may seem like a failure, but actually it is a sign of success. It means that the system has produced candidates that represent the most acceptable compromise of the conflicting opinions of the voters. If this process has worked perfectly, the results of the election will be a tie. Judging from the recent results of the American presidential election, democracy is working well.

Danny's argument for the statistical merits of two-party democracy seems to me to be completely sound when considered in an idealized political setting. But it ignores the reality of the contemporary American political landscape in which elections are invariably decided by much less rational considerations than Danny's article would have one believe.

To be more specific, the argument relies on a fundamentally unrealistic assumption: namely, that voters vote based on an analysis of the candidates' positions with respect to specific, definable issues — and the proximity of these positions to their own.

In fact, one has only to read the opinion polls or listen to interviews with voters to know that, overwhelmingly, voters cite much more qualitative reasons for choosing one candidate over another. So, Gore is "arrogant", "overbearing", "smart", or "well-informed"; Bush is "inexperienced", "immature", "compassionate", or "good-natured" (these were adjectives used to describe the candidates in actual interviews with voters conducted byThe New York Times during the course of the election). In fact, it is probably safe to say that a large percentage of voters aren't even aware of what the candidates' positions are on the issues. Of course, one cannot simply blame an uninformed electorate for this phemonemon. In many cases, the candidates purposely obfuscate their position on popular issues to improve their chances of getting elected. For instance, during the final 2000 presidential debate in East Lansing, Michigan, George W. Bush refused to say that he was against affirmative action, despite repeated questioning, choosing instead to say that he was for "affirmative access" — whatever that means. And then there is the fondness among politicians for stating their position on issues at such a level of abstraction as to become virtually meaningless. Hence, we have Republicans who claim to be "pro-family values", which leads one to the absurd conclusion that Democrats are "anti-family values". Conversely Democrats often claim to be "pro-environment" as if to say that Republicans are categorically "anti-environment".

Danny's argument would also have you believe that the ideal candidate should conduct polls on every important political issue, and simply adopt the more popular position. But, as we all know, campaigns aren't run this way. One reason for this is the fact that being perceived as wishy-washy and unprincipled may be more damaging to the candidate than supporting the "wrong" side of an issue. In other words, candidates are widely perceived to be more than the sum of their positions. Instead, we look to them to be principled leaders and steadfast in their convictions.

Two other reasons for candidates to ignore the polls are the influence of special interest groups in election politics, and in the case of presidential politics, the quirky nature of our (now infamous) electoral college system. While the majority of Americans clearly support tighter gun control laws, Al Gore rarely mentioned his support for such laws on the stump. Why? Because he knew the importance of winning the swing votes of Rust-Belt (Reagan) Democrats, many of whom happen to be gun owners. In the case of special interests, candidates are forced to downplay or obfuscate their true positions on issues (positions that may be supported by the majority of the electorate) because of the political influence that these special interests wield (again, one has to look no further than the NRA to find an organization that can be, at once, so out of touch with America's electoral majority, yet strike such fear in the hearts of politicians).

I think American Democracy is both better and worse than the idealized description Danny provides. On the one hand, I am, like many others, often dismayed by the influence of special interests in American electoral politics; I am frustrated by the sometimes superficial and haphazard manner in which the American electorate comparison shops for candidates; and I am frankly puzzled by the need to maintain our seemingly antiquated electoral college system. But I am also moved by the humanity of the American electoral process. Americans bring all sorts of rationales with them to the polls -- some sound, some misinformed. But on one day in November, they have an opportunity to pull a switch one way or the other, and God help those who try to predict the outcome. If this weren't the case, we might as well let one of Danny's supercomputers do the voting for us.

There is a popular view that says, "In the 2000 election, the popular vote seems so close to chance that it almost seems due to random chance — as though each voter was flipping a coin." A statistician might even suggest that "the difference has no significance."

Now, the theory of probability tells us that if 100 million votes were to come from flipping an "unbiased coin," we would expect the numbers of heads and tails to differ by only a few thousands. There will be only about one chance in a thousand that this will lead to a difference of more than 10,000 thousand votes. A difference of a million or more would be inconceivably unlikely.

However, in the previous century, the popular votes for the two major parties usually differed by several millions (except in '60 and '68). So, those people are not flipping unbiased coin, but show strong 'biases' that comes from many complex causes.

What could it mean, if anything, that in Florida, the popular vote differed by only a few hundred?ï The likely explanation for this is that the biases were biased themselves toward equality!

In other words, the more bias in the bias, the less chance to see for a close tie in the popular vote. A deeper analysis suggests that what happened in Florida was indeed an extremely unlikely event. For example, assume that the "will" of the 6 million Floridians might range uniformly from say 2 million to 4 million for each party. Then there would be only one chance in a thousand for this to lie within a thousand of votes of the center. If this is what happened, it asks for an explanation

I suspect that two new phenomena have entered the scene that has cause these numbers to come so close.

• The amounts of money for political campaigns have hugely increased.• The technical tools for making good polls have also improved.

So now, campaigners can better predict where spending their money will be most effective. They can pinpoint the critical districts in which voters will respond to particular issues, and then target them with more personalized persuasion techniques. (In other words, lie.) So, in effect, the budget for 'buying votes' has gone up, while the cost per such vote has gone down. This pushes the vote toward the center.

The Electoral College exacerbates this, because the campaigns can save money by not spending it in districts where the differences are too large to reverse. Consequently, huge amounts of money get focused at regions where they can be effective. (One formerly almost unknown new senator is said to have done this by spending what is estimated to be about 1000 dollars per vote.) And as soon as the difference changes its sign, the funding gets focused somewhere else.

One approach to a remedy is political:

• Reduce the magnitude of campaign spending.
• Abolish the Electoral College, which amplifies the effectiveness of targeted campaigns.ï

But neither of these seems feasible, because they'll be strongly opposed by incumbents.ï

Another approach is social:

• Educate the voters to refuse to cooperate with polls.
• Point out that it's in their interest to lie when they are being polled!

Yes, lying is reprehensible — although in this realm, it's traditional. The point is that if you're inclined toward Candidate X — but tell them that you favor Y — this induces your opposition to spend less in your district.

The problem isn't with the closeness of the election (which is a perfectly reasonable outcome, politically and statistically) or with the difficulties of the count (wherever this ends up, the margin of victory will be within any reasonable estimate of the margin of error), but with the disincentives to candidates of greater substance than these. The presidency is an office that is now open only to lifelong hypocrites of limited imagination, willing to surrender privacy and personal life in order to achieve limited power, the undivided attentions of potential assassins, and remarkably paltry financial reward.

Professor Emeritus, Stevens Institute of Technology; Former Staff Writer, the New Yorker

The situation with the Florida election vote is quite clear. There is no system of counting votes that is accurate enough to determine a winner when six million votes are cast and the difference is less than a thousand. Within any sensible margin of error you have a tie. Therefore what is needed is a system to deal with ties. Obviously this is a run off. I am quite certain that if the same people who voted the first time were to vote to break a tie it would have happened and how these votes were counted — by machine or human — would have been irrelevant. The matter would long ago have been settled and we could all get on with it.

Professor of Physics, Institute for Advanced Study; Author, Many Colored Glass; The Scientist as Rebel

For your entertainment, here is a piece by George Dyson. It shows the way to deal equitably with the situation in Florida. It was written three years ago and it is being published this week in the Bellingham Herald and in the Frankfurter Algemeine Zeitung. You might consider it an addendum to Danny Hillis's piece in the news-letter about "How Democracy Works". It describes a real case verifying Hillis's theory of democracy. Implications for biology, engineering, and physics are enormous.

HP Fellow and Director of the Systems Research Center at Hewlett Packard Laboratories

Concerning Danny Hillis' arguments on "How Democracy Works (Or Why Perfect Elections Should All End In Ties) " I'd like to point out that they are well known in political science. As a matter of fact, there is even a theorem (can you imagine, a theorem in political science?) that states it all rigorously. This so called median-voter theorem states that if two parties are trying to maximize their share of the votes, the only Nash equilibrium (each party making a best response to the other candidate's choice) is where both candidates chose the platform of the median voter's ideal policy.

While the assumptions underlying this theorem, originally proved by Hotelling in the context of consumer preferences in 1929, are rather stark — but not different from Danny's example — (it is assumed that voters have single-peaked preferences over a left to right one-dimensional issue space, and that everyone turns out and votes for the candidate whose platform they prefer), it turns out that the theorem's conclusion is robust in many respects. That is, modest departures from most of the canonical assumptions lead to only small changes in the candidates' behavior.

The present presidential platforms, while far from fitting the classical assumptions exactly, seem to indicate that the median voter theorem applies to even more general cases.

Danny's analysis is exactly right for sincere players. When the players are insincere, the story gets more complicated.

My sense of the 2000 presidential election is that some right-leaning Bush supporters believed their candidate was being insincere on the campaign trail, but with a welcome wink. For instance, opponents of gun control believed that once in office Bush would become an active ally, even though he was able to remain remarkably soft spoken, almost to the point of inaudibility, on gun control during the campaign. The same dynamic played out in reverse for Gore, however. Gore's most left-leaning potential supporters doubted his resolve or sincerity on issues such as protection of the environment.

Thus the perception of sincerity became the deciding factor in an election where both candidates sought the center. In some cases an appearance of selective insincerity actually helped a candidate (as in Bush's courting of the pro-gun vote).Speaking technically, Grover's algorithm show quantum search is only polynomially faster than classical search. Part of my research is solving continuous problems on a quantum computer and here there are problems which can be solved exponentially faster on a quantum computer.

To state the obvious, actual sincerity is quite a different thing from the appearance of sincerity. I know Gore a bit and find him to be utterly sincere in person, but sadly artificial on television. I'll turn to Phil's remarks. He says "Why does the quantum computer do new things? Why is complexity theory such a poor quide to the real world of problems?"

Childhood play is often concerned with the management of the appearance of sincerity. Children learn to present and detect poker faces, for example.

The most successful politicians not only excel at such skills, but even master elaborations, like sincerely displaying to one set of people one's insincerity to another, even if one has to be insincere to do so, and thus cementing an alliance.

The fact that the votes in a surprising number of diverse states came out almost perfectly tied demands further analysis. Maybe the arts and sciences of demographic-driven campaigning have become perfected to the point that there is almost no noise left in the system. I am reminded of the flat wall that can form between two soap bubbles.

Science Historian; Author, Turing's Cathedral: The Origins of the Digital Universe; Darwin Among the Machines

In the digital universe, every bit makes a difference. In a democracy, every vote counts. Punched card ballots are where these two universes coincide. On November 4, 1997, in Ferndale, Washington, the difference between two candidates for city council came down to one bit of difference on one card.

"There's not much case law on this," argues Frank J. Chmelik. "The responsibility of the canvassing board is to certify that universe of ballots that make up the count. A recount is to re-count the ballots. It doesn't make any sense to expand the universe of ballots. It would frustrate the purpose of the law to allow the recounting of an infinite set of ballots. It may have been in a sealed envelope but it was in a white envelope, not a pink envelope." It is December 19, 1997 and I am in Whatcom County Superior Court, listening to arguments before Judge Michael Moynihan in the matter of Yvonne Goldsmith vs. the Whatcom County Canvassing Board. Yvonne Goldsmith came in one vote ahead of Lloyd Zimmerman in the race for Ferndale City Council on election night. After a mandatory manual recount and the discovery of a lost ballot, she is now one vote behind. Her lawyers have appealed for a second recount, this time by machine. Said machine to be a Documation card reader, one of the models now built by Cardamation of Phoenixville, Pennsylvania — if the appeal is upheld. Right now the lawyers are arguing over whether to include an absentee ballot — discovered in a sealed envelope at the time of the first recount — whose validity depends in part on whether the envelope it turned up in was white or pink.

"It doesn't make any sense for a subsequent computer recount to supersede the manual recount," argues Karen Frakes on behalf of Whatcom County Auditor Sheila Forslof, returning to the issue of human beings vs. machines. "We have no reason to believe the computer recount will be any different."

Chmelik, however, cites chapter and verse of a statute (RCW 29.64.010) which "allows for second recount upon application by the candidate, who may specify such recount be done manually or by (electronic) vote tally machine. Goldsmith has a right to an electronic recount that will control."

Judge Moynihan, who is reading the fine print, refers to a clause (RCW 29.62.050) which "stipulates `a recount by machine shall use separate and distinct programming.' Can you explain?" Chmelik explains how the vote counting software will be freshly installed (under Windows 95) from a copy delivered from the State Capitol under official seal.

After some deliberation the judge decides: "They have to count that ballot. As to whether or not the candidate is entitled to an electronic or manual recount — she's entitled to make that choice. If there's a discrepancy, well, it will probably have to be decided by another court."

The recount (by machine) is scheduled for Tuesday, December 23, at 9:00 a.m. I arrive at the Whatcom County Courthouse at the appointed time and am ceremoniously signed into the room. No one, as far as I can tell, has ever heard of Wired magazine. The Bellingham Herald, a few blocks away, hasn't bothered to send a reporter but is awaiting the results by phone. The card reader sits facing the end of a long boardroom table, with various officials arrayed on either side. The reader is hooked up to an IBM 300GL PC, with the "separate and distinct programming" occupying an external Iomega Zip Drive. The software, produced by Computer Elections of Benicia, CA, is up and running under Windows 95.

Pete Griffin, elections supervisor, is fiddling with the card reader. He's proud of how much the machine cost and that it's recently been factory rebuilt. A number of minor dignitaries are present, as well as representatives for the two candidates and two official scrutineers. Lots of sealing and unsealing of metal boxes containing the ballots, with forms signed and witnessed in triplicate every time a deck of punched cards makes a move. The card reader is fired up. It runs through a series of "Logic and Accuracy" test decks from the Secretary of State. The results are compared with the results from election night, when the Logic and Accuracy decks were placed under the seals we just removed. It's a cryptic process, and we all just take the word of Peter Griffin that the string of characters generated on the monitor means everything's OK. The reader flutters smoothly through the piles of cards without missing a single beat — far smoother than the readers I saw at Cardamation, being tested against cards that had been stored for many years.

Finally, it's time to count the ballots. It doesn't take long, a few minutes at most. We all hold our breath. The manual recount was repeated three times, under strict supervision, and all three counts showed Zimmerman one vote ahead. Is this the moment of truth? I'm watching the floor under the machine, to see how many bits of "chad" — the card stock that is punched out to make a hole — fall out when running through the decks. Occasionally, in running through the vacuum-fed reader at high speed, a bit will be dislodged from a ballot. This is a problem with partially pre perforated ballots — and human beings who sometimes start to punch out one location and then change their mind. As Larry Olsen, the Republican observer, whispers to me when he senses what I'm thinking, "If chad falls out there's no way to put it back."

I count nine bits of chad on the carpet after all the ballots are run. The chad may just have fallen innocently out of the innards of the machine, it may have fallen out of any number of punch positions which had nothing to do with the city council race, or one or more bits might have fallen out of the Zimmerman-Goldsmith positions. Who knows? The seconds tick by, and I am acutely conscious at this instant that language and reality sometimes coincide: in the punched card universe a "bit" really is a bit, and Gregory Bateson's definition of information as "any difference that makes a difference" is true indeed, as we await the count of how many bits of difference between card and not-card have just passed through the Cardamation machine. Pete Griffin sits down at the PC, enters some commands, navigates through some dialog boxes, and a Hewlett-Packard laser printer begins to hum. It's a tie: 954 to 954. The statistics show one "overvote" — a ballot where both candidates have received a vote. Someone asks Goldsmith's representative if she would like to run the cards again. No.

The auditor consults the Laws of the State of Washington and announces that the election will now be decided by flipping a coin. The candidate who filed first — Goldsmith — gets to call it heads or tails. Three days later, Judge Moynihan tosses a 1921 silver dollar in the air. Goldsmith calls it tails — and wins. Goldsmith gets the seat on City Council, while the Judge awards Zimmerman the coin. The "Logic and Accuracy" decks go back, under seal, to the Secretary of State. We live in a binary universe — and what isn't governed by logic is governed by chance.

Luyen Chou is correct is pointing out that the model I used to explain ties is very much simpler that reality. However, I do not believe that the factors he describes interfere with feedback mechanisms described in the essay. It is certainly true that voter preference is determined by many factors, and that many of these factors are not under control of the candidates. This means that the candidate must use the variables that are under their control to achieve electablilty. If the candidates have many such issues to choose from, they may very well adopt different stances on particular issues to achieve the same net effect. Thus, both candidates may be in the optimally electable position in spite of holding very different positions on a particular issue, and spite of other voter preference factors that are beyond their control.